"Oracle believes the prospects for a successful mediation will be far greater if Google's executive-level representative is a superior to Mr. Rubin, who is the architect of Google's Android strategy -- the strategy that gives rise to this case," Oracle wrote in a Wednesday evening filing.

It also noted that Rubin has represented Google in past, failed mediations.

Now it's up to the magistrate judge, Paul Singh Grewal, to decide which executives should appear. In his Thursday order, Alsup referred the mediation to Grewal and recommended that he order Ellison and Page, as well as the executives the companies already suggested, to attend. But he said the final determination is up to Grewal.

The mediation sessions should take place this month, given that the case is set to go to trial on Oct. 31, Alsup wrote.

The companies have been battling about the way that Android handles Java applications. Oracle accuses Google of copying its code in Dalvik, the virtual machine in Android that runs applications. Google denies any wrongdoing.